Abstract

A mapping f:X→Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f−1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.